Hybrid VARIMA–Machine Learning Models for Multivariate Macroeconomic and Energy Forecasting

Accurate forecasting of macroeconomic and energy-related time series remains chal lenging due to structural instability, strong cross-dependencies, and pronounced deviations from linear Gaussian assumptions. While VARIMA models offer a transparent multivari ate framework, their empirical performance is often limited in environments characterized by volatility clustering and nonlinear adjustment dynamics. Conversely, machine learn ing methods provide greater flexibility but may suffer from instability and limited inter pretability in multivariate economic settings. This paper proposes a hybrid multivariate forecasting framework that combines VARIMA models with machine learning algorithms in a residual-based architecture. VARIMA is used as a disciplined linear filter to capture common dynamics across macroeconomic, financial, and energy variables, while machine learning models learn nonlinear corrections from the multivariate residuals. The approach is evaluated using monthly data spanning January 1999 to August 2025, including multi ple crisis episodes and a turbulent out-of-sample period. Extensive diagnostic tests reveal systematic violations of linear model assumptions, motivating hybridization. Forecasting results show that hybrid VARIMA–machine learning models consistently outperform both standalone VARIMA and pure machine learning specifications in terms of accuracy and robustness. The findings demonstrate that residual-based hybridization provides an inter pretable and effective strategy for integrating machine learning into multivariate economic forecasting.